Compactly generated t-structures in the derived category of a commutative ring
Commutative Algebra
2018-08-08 v3 K-Theory and Homology
Abstract
We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence between the compactly generated t-structures and infinite filtrations of the Zariski spectrum by Thomason subsets. Moreover, we show that in the case of a commutative noetherian ring, any bounded below homotopically smashing t-structure is compactly generated. As a consequence, all cosilting complexes are classified up to equivalence.
Cite
@article{arxiv.1806.00078,
title = {Compactly generated t-structures in the derived category of a commutative ring},
author = {Michal Hrbek},
journal= {arXiv preprint arXiv:1806.00078},
year = {2018}
}
Comments
26 pages. Corrected an error from the previous version, resulting in reformulation of the main results, and a new section